Radiolab’s show on “Stochasticity” offers entertaining examples to explain the concept of randomness. The story starts with the example of a 10 year old girl named “Laura Buxton” who released a balloon with a message: “Return this balloon to Laura Buxton.” The girl who received the balloon when it came down many miles away was another 10 year old girl named “Laura Buxton.” There were many other coincidences between the two Laura Buxtons.
Contrary to the assumptions of most people, randomness involves results that look like patterns. What about getting seven heads in a row? If you were only flipping the coin seven times, this can happen only one time out of 100, but if you get seven heads in a row somewhere in the process of flipping a coin 100 times, you can expect this to happen one time out of six, not improbable.
Another example is the case of Evelyn Adams, who one the lottery twice in two consecutive years. If you look only at whether this will happen twice with the purchase of two tickets, it would only happen once in 17 trillion times. If you consider the entire universe of people who buy lottery tickets, the question becomes “what are the odds that somebody somewhere will win the lottery twice?” The answer to that question is that it would be surprising if that didn’t happen repeatedly, and it has happened repeatedly (listen to minute 17 of the show).
The lesson? (at minute 19) “If you don’t see past yourself [to look at the big picture], you become prey to superstition.”
In the case of the Laura Buxtons, the story becomes much more interesting when we focus only on the similarities of the two girls and downplay the many many things they don’t have in common. But of course, listing their dissimilarities would not have been a good story, yet we prefer to believe in “magic” (see min 20).
See also, this post on patternicity.